Reddit mentions of Constructive Playthings Large Wooden Colored 1" Stringing Beads in Common Geometric Shapes with Two 36" L. Plastic Tipped Laces for Ages 3 Years and Up

For a child, you definitely want a clasp that breaks away easily to keep the necklace from becoming a choking hazard. Maybe that is why the ones at the store break so easily? I personally have not used the magnetic clasps, but that seems like it would be a good idea as long as you are sure she will not try to swallow these if she does end up breaking the necklace.

I personally like elastic string/thread or stretchy string for younger children as it can be pulled a fair amount before it breaks. Using a breakaway clasp should limit the possibility that it will break. You should be able to buy something like this in any craft store and in a variety of thicknesses to match the beads. You may want to skip the adult jewelry/bead area and head to the children's section first to see what craft materials they have available that are more age appropriate.

My concern regarding the beads would again be the choking hazard, so you might forego the beads for now and when she is old enough, let her string her own beaded necklace. Some places do sell large, wooden block-type beads that may be big enough to not fit in her mouth, but I am not sure how comfortable it would be for regular use.

This bead lace looks pretty sturdy: http://www.michaels.com/easy-beads-bead-lace-assorted-colors/10105013.html#q=beads&start=19

Here's an example of stretch cord: http://www.michaels.com/10205861.html#q=beads&start=21

Here's an example of the large wooden beads: http://www.amazon.com/Constructive-Playthings-Large-Wooden-Colored/dp/B0035Y7BIW

And finally, here's just some simple plastic beads that are sold in lots of sets for kids: http://www.michaels.com/creatology-bead-sample-pack-tropical-hearts/10187167.html

Hopefully someone with more experience can chime in. Otherwise, I'd be happy to try to help answer any other questions you may have.